552 Wolff—The Unsteady Motion of Viscous Liquids. 
Solving this equation* and determining the constants on the 
supposition that 1 = 1 when v = 0, we get, 
v -f Al ^ 2 
: ) 
— e 
A 2 
Up 2 A (v + Al) 
(^ 1+^3 
(v + Al)* , 
F t ~ 
F 
i (i>4 - Aiy 
2 A 2 
( 1+ 1/3 ^F + 
1 A* 
+ •••) = 0 , ( 8 ). 
5 L» F 2 
F 
5 L 2 F 2 
where -d = and F 
% a 
2 £> 
it a 2 p 
This last equation would give the actual velocity were it not 
for two things. First, it takes into account the hydrostatic 
pressure only, to which must be added the influence of the me¬ 
niscus. This acts as a negative pressure, and probably as a 
variable one. The variation is probably so small that no diffi¬ 
culty would be experienced in taking proper account of this ele¬ 
ment of the problem. Second, the equation (7) was derived 
from expressions which require the velocity in the tube to be a 
function of the distance from the wall of the tube. But the 
meniscus acts as a wall or diaphragm, preventing the liquid 
immediately behind it from moving more rapidly along the 
axis of the tube than along the walls of the tube. This re¬ 
tarding influence is very important, and equation (8) furnishes 
the basis for an experimental determination of its amount. 
Equation (8) must first be plotted, using v and l as the coordi¬ 
nates. Similar graphs must then be constructed from exper¬ 
imental data. The discrepancies between the two curves will 
indicate the retarding influence due to the meniscus. 
If as before the tube should connect two reservoirs, and a 
bubble of air should be admitted at one end and allowed to flow 
along, the effect due to the pull of the meniscus would be elim¬ 
inated, because there would be one pulling in one direction and 
one in the other. 
* The type of this equation may be found in W. Heymann’s Studien 
uber die Transformation und Integration der Differential und Dif - 
ferenzengleichungen; Leipsic, 1891, p. 28. 
